Labouchere System

Henry du Pré Labouchère was a nineteenth century English diplomat and politician, as well as an accomplished publisher and writer, and it is to him that the invention of the Labouchère betting system is ascribed.

This system, which is sometimes referred to colloquially as Labby, is a negative progression system for any type of roulette that uses outside even money bets (since these give the best odds of winning). It is based on the same principle as the Martingale system, but is designed to have a much less rapid progression: where the required amount of chips in Martingale increases geometrically, the Labouchère betting system only increases arithmetically.

How the system works

The Labouchère system is also known as the "Cancellation system" because it relies on a series of numbers, each of which have to be cancelled out in order for the system to end (and win). A player starts by choosing a series of numbers, for instance 1-2-2-3-1. This series can be as long as the player wants, containing whatever numbers he wants, this is all up to the player. Every bet made is an outside even money wager (red, even, etc.) of the sum of the first and the last number (1+1 = 2 in our example). If the bet wins, the two numbers are crossed out from the list (and cancelled) and another bet with the new first and last number is made. If the bet loses, its amount is added as a new number at the end of the series and a new bet is made. Once enough numbers have been cancelled out, the system will begin to make a profit. Once this happens the system can be started over again.

The system in action

Let’s see how the Labouchère works with a small example. We use the series 1-2-2-3-1, and always bet the same outside even money bet, for instance black. Here’s what will happen with the following streak of losses and wins: L-L-W-L-W-W-L.

  1. We bet the sum of the first and last number, that’s 2, on an even money bet (say, black). We lose.
    Net profit: -2
  2. We add the lost bet as a new number to the series, which now becomes 1-2-2-3-1-2. As our second wager we well bet the new first and last number: 1+2 = 3. We lose again.
    Net profit: -2-3 = -5
  3. Once more we add a new number and our list becomes 1-2-2-3-1-2-3. That means our next wager is 4. We win!
    Net profit: -2-3+4 = -1
  4. So now we must cancel the first and last number from the series, which becomes 2-2-3-1-2. That means the next bet is again 4. We lose…
    Net profit: -2-3+4-4 = -5
  5. We must add the 4 to the list which now is 2-2-3-1-2-4. The sum of the first and last numbers is 6, which is what we bet. This time we win!
    Net profit: -2-3+4-4+6 = +1
  6. We have made a profit! That means we can stop, be let’s assume we keep going. Since we won, the terminal numbers are cancelled and the list becomes 2-3-1-2. Our next bet then must be 2+2 = 4. We win again!
    Net profit: -2-3+4-4+6+4 = +5
  7. An even bigger profit. It would probably be wise to quit now, but if we go on this will happen: we cancel out the two 2’s and the list becomes 3-1. The sum is bet, which is again 4. But now we lose…
    Net profit: -2-3+4-4+6+4-4 = +1

Let’s end the example here. The list is not finished, but it does not have to be in order to stop playing or start over with a new list. The important thing is that we made a profit with more losses than wins. But in order to win 1 chip, we needed to start with at least 11 (at one point, we were down 5 and needed to bet 6).

Advantages and drawbacks

The greatest advantage of Labouchère, which is the reason for the system’s immense popularity, is of course the fact that players can decide for themselves the speed of the progression. What that means is that, unlike in Martingale, the size of the bets (and therefore the size of the required bankroll) can increase rather gently. By using a shorter list with higher numbers, players can play more aggressively if they want to. This does require a player to win several times in order to cover his losses, but not as many as in for instance Oscar's Grind.

The single major drawback lies in the fact that arithmetic progression of bet size can still lead to loss larger than can be recovered at the table. Even if the amount of chips required to play the system increases rather slowly, a long enough streak of losses can easily bankrupt the player, and the chances of this happening at some point in time are 100%…

Minimizing risk for the Labouchère system

As noted before, the great thing about the Labouchère betting system is that it allows for extensive manipulation by the player. We will consider two strategies that can be used to customize the system to your liking.

  • Designing a good initial series
    Those first numbers a player decides to include in his series for a large part determine the course of the game, and it’s wise to keep the following things in mind:

    • How much you want to win: if you were to keep playing until you had cancelled out all the numbers on the list, your net profit would be the sum of the numbers on your initial list. The higher this sum is, the larger the chances of running out of budget.
    • The largest possible numbers on the list: if we keep playing until all numbers have been cancelled, at least half of our initial list will have been the first number. And every time we lose, the bet is increased with the first number. The higher this is, the faster the bets will increase and the faster we will hit the table maximum. So keep the initial series in relation to your bankroll and the betting max.
  • Dividing too large bets
    If the maximum bet at the table is not very high, the system can encounter the problem where some required bets are too large and may not be placed. This can be circumvented by dividing the numbers you add to the series. If we lose a bet of 12, we could instead of writing down this number at the end of the series, simply write 4-4-4 and add not one but three numbers. If you divide large numbers in such a way you always add less than half the maximum bet, you will never run the risk of exceeding it. The problem here is of course that this will require a lot more winning spins, and at some point our bankroll will also run out and the losses would still be unrecoverable.

As with all roulette betting systems, it is always prudent to set a budget and simply stop playing and take a break when losses get too high. Remember roulette is a game and it’s supposed to be fun!